The aim of this thesis is to research the use of Computational Fluid Dynamics (CFD) as design tool to predict fluid flow across stationary and moving bluff bodies. The principle of moving meshes is introduced to move the body vertically with respect to time. The moving mesh idea is first tested on a square body with a coarse discretized flow domain for transient conditions. The results can be animated to see how the flow pattern and mesh change with time. The idea is then implemented on a cylinder with a very fine mesh to capture the build-up and dispersion of vortices being shed from the cylinder as it moves cyclically for transient conditions. With this first approach a bluff body is forced to move cyclically with respect to time in cross flow. Many possibilities now exist to apply this idea further for other applications where forced vibration is important.The next approach is to use CFD to simulate flow-induced vibrations of bluff bodies. The pressure force on the bluff body is considered as a first approach to solve this problem. The inertia mass of the body balancing the effect of the pressure force on the body is first used, but the results indicate that damping and stiffness also have to be considered to obtain more realistic results. The effect of the pressure force on the body shows generally a downwards movement of the body for the first period of simulation and in the case of the square, after six time steps of the period of simulation the .pressure force switches to a positive value with resulting upwards movement of the body. The effect of the total force (shear + pressure) on a bluff body is not presented in this thesis. CFD as design tool is researched for various bundle configurations of cylinders. A new concept of split cylinders is researched and the best configuration obtained for various horizontal and vertical spacings of downstream- and upstream cylinders and cylinder halves. Experimental results on cylinders in a - small scale wind tunnel are used to compare the numerical results with the obtained pressure distribution around a stationary cylinder and the concept of velocity distribution over and between a split cylinder. Further development of the numerical flow model is necessary to include elasticity and longer three dimensional spanwise lengths of the object to obtain predictions of real flow-induced vibrations of bluff bodies. This first approach of numerical predictions of flow across stationary and moving bluff bodies creates many possibilities of complementing experimental results and comparing the obtained results with each other.